Finite Group Databasebeta

← C2×#23772388 #35152736

Subgroups — C2×#23772388 #35152736

Order 20224.

2026 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099093C211yesmaximal, characteristic
2#23772388C2116yesmaximal, direct product factor
3C2×#19098693C211yesmaximal, characteristic, complemented
4C2×#19098692C211yesmaximal, characteristic, complemented
5C2×#19098637C211yesmaximal, characteristic, complemented
6C2×#19098635C211yesmaximal, characteristic, complemented
7C2×#19098634C211yesmaximal, characteristic, complemented
8C2×#19098634C211yesmaximal, characteristic, complemented
9C2×(C22⋊D79)⋊C8C211yesmaximal, characteristic, complemented
10C2×#19098623C211yesmaximal, characteristic, complemented
11C2×#19098621C211yesmaximal, characteristic, complemented
12C2×#19098613C211yesmaximal, characteristic, complemented
13C2×#19098518C211yesmaximal, characteristic, complemented
14C2×#19098517C211yesmaximal, characteristic, complemented
15C22×#14579071C211yesmaximal, characteristic, complemented
16C2×C8×D4×C79C211yesmaximal, characteristic, complemented
17C22×#11929608C2211yescharacteristic
18C22×#11929607C2211yescharacteristic
19C23×C79⋊C8C2211yescharacteristic
20C22×C8×D79C2211yescharacteristic
21#19099093C418yes—
22#19099093C2218yes—
23C2×#14579156C411yescharacteristic
24C2×#14579154C411yescharacteristic
25C2×#14579151C411yescharacteristic
26C2×#14579147C411yescharacteristic
27C2×#14579145C411yescharacteristic
28C2×#14579142C411yescharacteristic
29C2×#14579138C411yescharacteristic
30C2×#14579133C411yescharacteristic
31C2×C4×Dic158C2211yescharacteristic
32C2×C4×C22⋊D79C2211yescharacteristic
33C2×C4×C22⋊D79C2211yescharacteristic
34C2×#14579120C2211yescharacteristic
35C2×#14579118C2211yescharacteristic
36C22×C4×Dic79C2211yescharacteristic
37#19098693C2218yescomplemented
38#19098692C2218yescomplemented
39#19098637C2218yescomplemented
40#19098635C2218yescomplemented
41#19098634C2218yescomplemented
42#19098634C2218yescomplemented
43(C22⋊D79)⋊C8C2218yescomplemented
44#19098623C2218yescomplemented
45#19098621C2218yescomplemented
46#19098613C2218yescomplemented
47C2×C4⋊(C79⋊C8)C2211yescharacteristic
48C2×Dic79⋊C8C2211yescharacteristic
49C2×Dic79⋊C8C2211yescharacteristic
50C2×Dic79⋊C8C2211yescharacteristic
51C2×Dic79⋊C8C2211yescharacteristic
52C2×C22⋊(C79⋊C8)C2211yescharacteristic
53C2×C22⋊(C79⋊C8)C2211yescharacteristic
54C2×(C2×D79)⋊C8C2211yescharacteristic
55C2×(C2×D79)⋊C8C2211yescharacteristic
56#19098518C2218yescomplemented
57#19098517C2218yescomplemented
58C2×#14579072C2211yescharacteristic
59C2×#14579071C2211yescharacteristic
60C2×#14579071C2211yescharacteristic
61C2×#14579071C2211yescharacteristic
62C2×#14579071C2211yescharacteristic
63C2×#14579071C2211yescharacteristic
64C2×#14579071C2218yescomplemented
65C2×C8×Dic79C2211yescharacteristic
66C2×C8×Dic79C2211yescharacteristic
67C2×C8×Dic79C2211yescharacteristic
68C23×C8×C79C2211yescharacteristic
69C23×C8×C79C2211yescharacteristic
70C2×C4×D4×C79C2211yescharacteristic
71C8×D4×C79C2218yescomplemented
72C2×C4⋊C8×C79C2211yescharacteristic
73C2×C22⋊C8×C79C2211yescharacteristic
74C2×C22⋊C8×C79C2211yescharacteristic
75C2×C4×C8×C79C2211yescharacteristic
76C22×Dic158C2×C411yescharacteristic
77C22×C22⋊D79C2×C411yescharacteristic
78C22×C22⋊D79C2×C411yescharacteristic
79C23×Dic79C2×C411yescharacteristic
80C23×Dic79C2×C411yescharacteristic
81C22×C4×D79C2311yescharacteristic
82C2×#11929608—24no—
83C2×#11929608C2314yes—
84C2×#11929607—24no—
85C2×#11929607C2314yes—
86C22×C79⋊C8—24no—
87C22×C79⋊C8C2314yes—
88C22×C79⋊C8C2311yescharacteristic
89C22×C79⋊C8C2311yescharacteristic
90C22×C79⋊C8C2311yescharacteristic
91C22×C79⋊C8C2311yescharacteristic
92C2×C8×D79—24no—
93C2×C8×D79C2314yes—
94#14579156C2×C418yes—
95#14579154C2×C418yes—
96#14579151C2×C418yes—
97#14579147C2×C418yes—
98#14579145C2×C418yes—
99#14579142C2×C418yes—
100#14579138C2×C418yes—
101#14579133C2×C418yes—
102C4×Dic158C2×C414yes—
103C4×Dic158C2314yes—
104C4×C22⋊D79C2×C414yes—
105C4×C22⋊D79C2×C414yes—
106C4×C22⋊D79C2314yes—
107C4×C22⋊D79C2314yes—
108#14579120C2×C414yes—
109#14579120C2314yes—
110#14579118C2×C414yes—
111#14579118C2314yes—
112C2×C4⋊Dic79C2×C411yescharacteristic
113C2×C4⋊Dic79C2×C411yescharacteristic
114C2×C4⋊Dic79C2×C411yescharacteristic
115C2×Dic79⋊C4C2×C411yescharacteristic
116C2×Dic79⋊C4C2×C411yescharacteristic
117C2×Dic79⋊C4C2×C411yescharacteristic
118C2×Dic79⋊C4C2×C411yescharacteristic
119C2×Dic79⋊C4C2×C411yescharacteristic
120C2×Dic79⋊C4C2×C411yescharacteristic
121C2×C22⋊Dic79C2×C411yescharacteristic
122C2×C22⋊Dic79C2×C411yescharacteristic
123C2×C22⋊Dic79C2×C411yescharacteristic
124C2×C22⋊Dic79C2×C411yescharacteristic
125C2×(C2×D79)⋊C4C2×C411yescharacteristic
126C2×(C2×D79)⋊C4C2×C411yescharacteristic
127C2×(C2×D79)⋊C4C2×C411yescharacteristic
128C2×(C2×D79)⋊C4C2×C411yescharacteristic
129C2×C4×Dic79C2×C411yescharacteristic
130C2×C4×Dic79C2×C411yescharacteristic
131C2×C4×Dic79C2×C414yes—
132C2×C4×Dic79C2311yescharacteristic
133C2×C4×Dic79C2311yescharacteristic
134C2×C4×Dic79C2314yes—
135C2×C4×Dic79C2311yescharacteristic
136C4⋊(C79⋊C8)C2314yes—
137Dic79⋊C8C2314yes—
138Dic79⋊C8C2314yes—
139Dic79⋊C8C2314yes—
140Dic79⋊C8C2314yes—
141C22⋊(C79⋊C8)C2314yes—
142C22⋊(C79⋊C8)C2314yes—
143(C2×D79)⋊C8C2314yes—
144(C2×D79)⋊C8C2314yes—
145#14579072C2314yes—
146#14579071C2314yes—
147#14579071C2314yes—
148#14579071C2314yes—
149#14579071C2314yes—
150#14579071C2314yes—
151C8×Dic79C2314yes—
152C8×Dic79C2314yes—
153C8×Dic79C2314yes—
154C22×D4×C79C2×C411yescharacteristic
155C23×C4×C79C2311yescharacteristic
156C23×C4×C79C2311yescharacteristic
157C22×C8×C79—24no—
158C22×C8×C79—24no—
159C22×C8×C79C2311yescharacteristic
160C22×C8×C79C2311yescharacteristic
161C22×C8×C79C2314yes—
162C22×C8×C79C2314yes—
163C22×C8×C79C2311yescharacteristic
164C22×C8×C79C2311yescharacteristic
165C4×D4×C79C2×C414yes—
166C4×D4×C79C2314yes—
167C2×C4⋊C4×C79C2×C411yescharacteristic
168C2×C22⋊C4×C79C2×C411yescharacteristic
169C2×C22⋊C4×C79C2×C411yescharacteristic
170C2×C42×C79C2311yescharacteristic
171C4⋊C8×C79C2314yes—
172C22⋊C8×C79C2314yes—
173C22⋊C8×C79C2314yes—
174C4×C8×C79C2314yes—
175C23×D79C22×C411yescharacteristic
176C2×Dic158—42no—
177C2×Dic158C22×C414yes—
178C2×C22⋊D79—24no—
179C2×C22⋊D79—42no—
180C2×C22⋊D79C22×C414yes—
181C2×C22⋊D79C22×C414yes—
182C22×Dic79—24no—
183C22×Dic79—42no—
184C22×Dic79C22×C411yescharacteristic
185C22×Dic79C22×C411yescharacteristic
186C22×Dic79C22×C411yescharacteristic
187C22×Dic79C22×C411yescharacteristic
188C22×Dic79C22×C411yescharacteristic
189C22×Dic79C22×C414yes—
190C22×Dic79C22×C411yescharacteristic
191C22×Dic79C22×C411yescharacteristic
192C22×Dic79C22×C414yes—
193C2×C4×D79—22no—
194C2×C4×D79—22no—
195C2×C4×D79C22×C412yes—
196C2×C4×D79C2412yes—
197#11929608—28no—
198#11929607—28no—
199C2×C79⋊C8—28no—
200C2×C79⋊C8—22no—
201C2×C79⋊C8—22no—
202C2×C79⋊C8—22no—
203C2×C79⋊C8#4114yes—
204C2×C79⋊C8C2412yes—
205C2×C79⋊C8C2412yes—
206C2×C79⋊C8C2412yes—
207C2×C79⋊C8C2412yes—
208C8×D79—28no—
209C4⋊Dic79C22×C414yes—
210C4⋊Dic79C22×C414yes—
211C4⋊Dic79C22×C414yes—
212Dic79⋊C4C22×C414yes—
213Dic79⋊C4C22×C414yes—
214Dic79⋊C4C22×C414yes—
215Dic79⋊C4C22×C414yes—
216Dic79⋊C4C22×C414yes—
217Dic79⋊C4C22×C414yes—
218C22⋊Dic79C22×C414yes—
219C22⋊Dic79C22×C414yes—
220C22⋊Dic79C22×C414yes—
221C22⋊Dic79C22×C414yes—
222(C2×D79)⋊C4C22×C414yes—
223(C2×D79)⋊C4C22×C414yes—
224(C2×D79)⋊C4C22×C414yes—
225(C2×D79)⋊C4C22×C414yes—
226C4×Dic79C22×C412yes—
227C4×Dic79C22×C412yes—
228C4×Dic79C22×C414yes—
229C4×Dic79C22×C414yes—
230C4×Dic79C22×C412yes—
231C4×Dic79C2412yes—
232C4×Dic79C2412yes—
233C4×Dic79C2412yes—
234C24×C79C22×C411yescharacteristic
235C24×C79C22×C411yescharacteristic
236C2×D4×C79—24no—
237C2×D4×C79C22×C414yes—
238C22×C4×C79—22no—
239C22×C4×C79—22no—
240C22×C4×C79—22no—
241C22×C4×C79—22no—
242C22×C4×C79C22×C411yescharacteristic
243C22×C4×C79C22×C411yescharacteristic
244C22×C4×C79C22×C411yescharacteristic
245C22×C4×C79C22×C411yescharacteristic
246C22×C4×C79C22×C412yes—
247C22×C4×C79C22×C412yes—
248C22×C4×C79C2412yes—
249C22×C4×C79C2412yes—
250C22×C4×C79C2411yescharacteristic
251C2×C8×C79—28no—
252C2×C8×C79—28no—
253C2×C8×C79—22no—
254C2×C8×C79—22no—
255C2×C8×C79—22no—
256C2×C8×C79#4114yes—
257C2×C8×C79C2412yes—
258C2×C8×C79C2412yes—
259C2×C8×C79C2412yes—
260C2×C8×C79C2412yes—
261C4⋊C4×C79C22×C414yes—
262C22⋊C4×C79C22×C414yes—
263C22⋊C4×C79C22×C414yes—
264C42×C79C22×C412yes—
265C42×C79C2412yes—
266C23×C79—22no—
267C23×C79—22no—
268C23×C79—22no—
269C23×C79—22no—
270C23×C79—22no—
271C23×C79#13114yes—
272C23×C79C23×C412yes—
273C23×C79C23×C412yes—
274C23×C79C23×C411yescharacteristic
275C22×D79—22no—
276C22×D79—22no—
277C22×D79—22no—
278C22×D79C23×C412yes—
279D4×C79—28no—
280C2×C4×C79—22no—
281C2×C4×C79—22no—
282C2×C4×C79—22no—
283C2×C4×C79—22no—
284C2×C4×C79—24no—
285C2×C4×C79—24no—
286C2×C4×C79—22no—
287C2×C4×C79—22no—
288C2×C4×C79—22no—
289C2×C4×C79—22no—
290C2×C4×C79C23×C412yes—
291C2×C4×C79C23×C412yes—
292C2×C4×C79C23×C412yes—
293C2×C4×C79C23×C412yes—
294C2×C4×C79C23×C411yescharacteristic
295C2×C4×C79C2×#4112yes—
296C2×C4×C79C2×#4112yes—
297C2×C4×C79C2511yescharacteristic
298C22⋊D79—28no—
299C22⋊D79—44no—
300C2×Dic79—22no—
301C2×Dic79—28no—
302C2×Dic79—22no—
303C2×Dic79—22no—
304C2×Dic79—22no—
305C2×Dic79—22no—
306C2×Dic79—22no—
307C2×Dic79—22no—
308C2×Dic79—44no—
309C2×Dic79C23×C412yes—
310C2×Dic79C23×C412yes—
311C2×Dic79C23×C412yes—
312C2×Dic79C23×C412yes—
313C2×Dic79C23×C412yes—
314C2×Dic79C23×C412yes—
315C2×Dic79C23×C412yes—
316C4×D79—24no—
317C4×D79—22no—
318C4×D79—22no—
319Dic158—44no—
320C8×C79—22no—
321C8×C79—22no—
322C8×C79—22no—
323C8×C79C2×#4114yes—
324C79⋊C8—22no—
325C79⋊C8—22no—
326C79⋊C8—22no—
327C79⋊C8C2×#4114yes—
328C22×C79—22no—
329C22×C79—28no—
330C22×C79—22no—
331C22×C79—22no—
332C22×C79—22no—
333C22×C79—22no—
334C22×C79—44no—
335C22×C79C4×#4112yes—
336C22×C79C2×#13114yes—
337C22×C79C2×#13112yes—
338C22×C79#56812yes—
339C22×C79C24×C411yescharacteristic
340C2×D79—22no—
341C2×D79—22no—
342C2×D79—22no—
343C2×D79—44no—
344C4×C79—22no—
345C4×C79—22no—
346C4×C79—22no—
347C4×C79—22no—
348C4×C79C4×#4112yes—
349C4×C79C22×#4111yescharacteristic
350C4×C79C22×#4111yescharacteristic
351Dic79—22no—
352Dic79—22no—
353Dic79—22no—
354Dic79—22no—
355Dic79—22no—
356Dic79—22no—
357Dic79—22no—
358C2×#2968—791nomaximal, Sylow
359C2×C79—24no—
360C2×C79—42no—
361C2×C79#296814yescomplemented
362C2×C79C2×C4×#4111yescharacteristic
363C2×C79C22×#13111yescharacteristic
364C2×C79C2×#56811yescharacteristic
365D79—42no—
366C2×#529—791no—
367#2968—7916no—
368C2×#446—791no—
369C2×#446—791no—
370C2×#435—791no—
371C2×#435—791no—
372C2×#435—791no—
373C2×#435—791no—
374C2×C8×D4—791no—
375C2×C8×D4D7911yescharacteristic, complemented
376C2×#433—791no—
377C2×#433—791no—
378C2×#431—791no—
379C2×#405—791no—
380C2×#405—791no—
381C22×#97—791no—
382C79C2×#296811yescharacteristic, complemented, Sylow
383C22×M16—791no—
384C22×M16—791no—
385C23×C8—791no—
386C23×C8—791no—
387C23×C8C2×D7911yescharacteristic
388C23×C8C2×D7911yescharacteristic
389#529—798no—
390#529—798no—
391C2×#126—791no—
392C2×#126—791no—
393C2×#125—791no—
394C2×#124—791no—
395C2×#123—791no—
396C2×#123—791no—
397C2×C22⋊Q8—791no—
398C2×#121—791no—
399C2×C4×Q8—791no—
400C2×C4×D4—791no—
401C2×C4×D4—791no—
402C2×C4×D4C2×D7911yescharacteristic
403C2×#117—791no—
404C2×#117—791no—
405C22×C42—791no—
406#446—798no—
407#446—798no—
408#435—798no—
409#435—798no—
410#435—798no—
411#435—798no—
412C8×D4—798no—
413C8×D4C2×D7918yescomplemented
414#433—798no—
415#433—798no—
416#431—798no—
417C2×C4⋊C8—791no—
418C2×C4⋊C8—791no—
419C2×C4⋊C8—791no—
420C2×C4⋊C8—791no—
421C2×C4⋊C8—791no—
422C2×C4⋊C8C2×D7911yescharacteristic
423C2×C22⋊C8—791no—
424C2×C22⋊C8—791no—
425C2×C22⋊C8—791no—
426C2×C22⋊C8—791no—
427C2×C22⋊C8C2×D7911yescharacteristic
428C2×C22⋊C8C2×D7911yescharacteristic
429#405—798no—
430#405—798no—
431C2×#97—791no—
432C2×#97—791no—
433C2×#97—791no—
434C2×#97—791no—
435C2×#97—798no—
436C2×#97—791no—
437C2×#97—791no—
438C2×C4×C8—791no—
439C2×C4×C8—791no—
440C2×C4×C8—791no—
441C2×C4×C8C2×D7911yescharacteristic
442C22×Q8—791no—
443C22×D4—791no—
444C22×D4—791no—
445C22×D4C4×D7911yescharacteristic
446C23×C4—791no—
447C23×C4—791no—
448C23×C4—791no—
449C23×C4C22×D7911yescharacteristic
450C23×C4C22×D7911yescharacteristic
451C2×M16—794no—
452C2×M16—794no—
453C2×M16—1584no—
454C2×M16—1584no—
455C22×C8—24no—
456C22×C8—24no—
457C22×C8—791no—
458C22×C8—794no—
459C22×C8—791no—
460C22×C8—791no—
461C22×C8—791no—
462C22×C8—794no—
463C22×C8—1584no—
464C22×C8—1584no—
465C22×C8C22×D7914yes—
466C22×C8C22×D7914yes—
467C22×C8C22×D7911yescharacteristic
468C22×C8C22×D7911yescharacteristic
469C22×C8C22×D7911yescharacteristic
470C22×C8C22×D7911yescharacteristic
471#126—798no—
472#126—798no—
473#125—798no—
474#124—798no—
475#123—798no—
476#123—798no—
477C22⋊Q8—798no—
478#121—798no—
479C4×Q8—794no—
480C4×Q8—794no—
481C4×D4—794no—
482C4×D4—794no—
483C4×D4—794no—
484C4×D4—794no—
485C4×D4C4×D7914yes—
486C4×D4C22×D7914yes—
487#117—794no—
488#117—794no—
489#117—794no—
490#117—794no—
491C2×C4⋊C4—791no—
492C2×C4⋊C4—791no—
493C2×C4⋊C4—791no—
494C2×C4⋊C4—791no—
495C2×C4⋊C4—791no—
496C2×C4⋊C4—791no—
497C2×C4⋊C4—791no—
498C2×C4⋊C4—791no—
499C2×C4⋊C4—791no—
500C2×C4⋊C4C4×D7911yescharacteristic
501C2×C22⋊C4—791no—
502C2×C22⋊C4—791no—
503C2×C22⋊C4—791no—
504C2×C22⋊C4—791no—
505C2×C22⋊C4—791no—
506C2×C22⋊C4—791no—
507C2×C22⋊C4—791no—
508C2×C22⋊C4—791no—
509C2×C22⋊C4C4×D7911yescharacteristic
510C2×C22⋊C4C4×D7911yescharacteristic
511C2×C42—791no—
512C2×C42—791no—
513C2×C42—794no—
514C2×C42—794no—
515C2×C42—791no—
516C2×C42—791no—
517C2×C42—791no—
518C2×C42C22×D7911yescharacteristic
519C4⋊C8—794no—
520C4⋊C8—794no—
521C4⋊C8—794no—
522C4⋊C8—794no—
523C4⋊C8—794no—
524C4⋊C8C22×D7914yes—
525C22⋊C8—794no—
526C22⋊C8—794no—
527C22⋊C8—794no—
528C22⋊C8—794no—
529C22⋊C8C22×D7914yes—
530C22⋊C8C22×D7914yes—
531#97—794no—
532#97—794no—
533#97—794no—
534#97—794no—
535#97—794no—
536#97—794no—
537C4×C8—794no—
538C4×C8—794no—
539C4×C8—794no—
540C4×C8C22×D7914yes—
541C24—791no—
542C24C2×C4×D7911yescharacteristic
543C24C2×C4×D7911yescharacteristic
544C2×Q8—3162no—
545C2×Q8—794no—
546C2×D4—24no—
547C2×D4—3162no—
548C2×D4—794no—
549C2×D4—794no—
550C2×D4—1584no—
551C2×D4C2×C4×D7914yes—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—3162no—
557C22×C4—794no—
558C22×C4—791no—
559C22×C4—791no—
560C22×C4—791no—
561C22×C4—791no—
562C22×C4—794no—
563C22×C4—791no—
564C22×C4—791no—
565C22×C4—791no—
566C22×C4—792no—
567C22×C4—792no—
568C22×C4—1584no—
569C22×C4—1582no—
570C22×C4—1582no—
571C22×C4C2×C4×D7911yescharacteristic
572C22×C4C2×C4×D7912yes—
573C22×C4C2×C4×D7911yescharacteristic
574C22×C4C2×C4×D7911yescharacteristic
575C22×C4C2×C4×D7911yescharacteristic
576C22×C4C2×C4×D7912yes—
577C22×C4C23×D7912yes—
578C22×C4C23×D7912yes—
579C22×C4C23×D7911yescharacteristic
580M16—1588no—
581M16—1588no—
582C2×C8—22no—
583C2×C8—22no—
584C2×C8—22no—
585C2×C8—28no—
586C2×C8—28no—
587C2×C8—794no—
588C2×C8—792no—
589C2×C8—792no—
590C2×C8—792no—
591C2×C8—792no—
592C2×C8—1588no—
593C2×C8—1588no—
594C2×C8—1582no—
595C2×C8—1582no—
596C2×C8—1582no—
597C2×C8#1192962314yes—
598C2×C8C23×D7912yes—
599C2×C8C23×D7912yes—
600C2×C8C23×D7912yes—
601C2×C8C23×D7912yes—
602C4⋊C4—794no—
603C4⋊C4—794no—
604C4⋊C4—794no—
605C4⋊C4—794no—
606C4⋊C4—794no—
607C4⋊C4—794no—
608C4⋊C4—794no—
609C4⋊C4—794no—
610C4⋊C4—794no—
611C4⋊C4C2×C4×D7914yes—
612C22⋊C4—794no—
613C22⋊C4—794no—
614C22⋊C4—794no—
615C22⋊C4—794no—
616C22⋊C4—794no—
617C22⋊C4—794no—
618C22⋊C4—794no—
619C22⋊C4—794no—
620C22⋊C4C2×C4×D7914yes—
621C22⋊C4C2×C4×D7914yes—
622C42—792no—
623C42—792no—
624C42—792no—
625C42—792no—
626C42—792no—
627C42—794no—
628C42—794no—
629C42—792no—
630C42C2×C4×D7912yes—
631C42C23×D7912yes—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—792no—
638C23—1582no—
639C23—1582no—
640C23—1582no—
641C23#1457916714yes—
642C23C22×C4×D7912yes—
643C23C22×C4×D7912yes—
644C23C22×C4×D7911yescharacteristic
645Q8—3164no—
646D4—28no—
647D4—3164no—
648D4—1588no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—24no—
654C2×C4—24no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—3164no—
660C2×C4—792no—
661C2×C4—792no—
662C2×C4—792no—
663C2×C4—792no—
664C2×C4—792no—
665C2×C4—792no—
666C2×C4—792no—
667C2×C4—1582no—
668C2×C4—1588no—
669C2×C4—1582no—
670C2×C4—1582no—
671C2×C4—1582no—
672C2×C4—1582no—
673C2×C4—1582no—
674C2×C4—1582no—
675C2×C4—1584no—
676C2×C4—1582no—
677C2×C4—1582no—
678C2×C4C22×C4×D7912yes—
679C2×C4C22×C4×D7912yes—
680C2×C4C22×C4×D7912yes—
681C2×C4C22×C4×D7912yes—
682C2×C4C22×C4×D7911yescharacteristic
683C2×C4#41×D7912yes—
684C2×C4C2×#1192962312yes—
685C2×C4C24×D7911yescharacteristic
686C8—22no—
687C8—22no—
688C8—22no—
689C8—794no—
690C8—1582no—
691C8—1582no—
692C8—1582no—
693C8C2×#1192962314yes—
694C22—22no—
695C22—22no—
696C22—28no—
697C22—22no—
698C22—22no—
699C22—22no—
700C22—44no—
701C22—3164no—
702C22—1582no—
703C22—1582no—
704C22—1582no—
705C22C4×#1192962312yes—
706C22C2×#1457916714yes—
707C22C2×#1457916712yes—
708C22#1909932812yes—
709C22C23×C4×D7911yescharacteristic
710C4—22no—
711C4—22no—
712C4—22no—
713C4—22no—
714C4—1582no—
715C4—1582no—
716C4—1582no—
717C4—1582no—
718C4—1582no—
719C4—1582no—
720C4—1582no—
721C4C4×#1192962312yes—
722C4C2×#41×D7911yescharacteristic
723C4C22×#1192962311yescharacteristic
724C2—24no—
725C2—42no—
726C2—3162no—
727C2#2377238814yesdirect product factor
728C2C2×C4×#1192962311yescharacteristic
729C2C22×#1457916711yescharacteristic
730C2C2×#1909932811yescharacteristic
subgroupG/H
centerC22×C4C23×D79
commutatorC22×C79C24×C4
FrattiniC2×C4C24×D79
FittingC2×C8×D4×C79C2
socleC23×C79C23×C4
prime radicalC2×#14579133C4
cosocleC2×C4×C79C25
hypercenterC2×C8×D4D79
hypocenterC79C2×#2968
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22×C4 ◁ C2×C8×D4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #23772388C2direct (N × H)
3. C2×#19098693C2semidirect
4. C2×#19098692C2semidirect
5. C2×#19098637C2semidirect
6. C2×#19098635C2semidirect
7. C2×#19098634C2semidirect
8. C2×#19098634C2semidirect
9. C2×(C22⋊D79)⋊C8C2semidirect
10. C2×#19098623C2semidirect
11. C2×#19098621C2semidirect
12. C2×#19098613C2semidirect
13. C2×#19098518C2semidirect
14. C2×#19098517C2semidirect
15. C22×#14579071C2semidirect
16. C2×C8×D4×C79C2semidirect
37. #19098693C22semidirect
38. #19098692C22semidirect
39. #19098637C22semidirect
40. #19098635C22semidirect
41. #19098634C22semidirect
42. #19098634C22semidirect
43. (C22⋊D79)⋊C8C22semidirect
44. #19098623C22semidirect
45. #19098621C22semidirect
46. #19098613C22semidirect
56. #19098518C22semidirect
57. #19098517C22semidirect
64. C2×#14579071C22semidirect
71. C8×D4×C79C22semidirect
361. C2×C79#2968semidirect
375. C2×C8×D4D79semidirect
382. C79C2×#2968semidirect
413. C8×D4C2×D79semidirect
727. C2#23772388direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#190990932
#237723882
C2×#190986932
C2×#190986922
C2×#190986372
C2×#190986352
C2×#190986342
C2×(C22⋊D79)⋊C82
C2×#190986232
C2×#190986212
C2×#190986132
C2×#190985182
C2×#190985172
C22×#145790712
C2×C8×D4×C792
C2×#296879